/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Strip Symbols Proof [SOUND, 0 ms] (2) QTRS (3) RFCMatchBoundsTRSProof [EQUIVALENT, 4 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: b(a(a(b(a(b(a(a(a(b(x1)))))))))) -> a(b(a(b(a(a(a(b(a(b(a(a(b(x1))))))))))))) Q is empty. ---------------------------------------- (1) Strip Symbols Proof (SOUND) We were given the following TRS: b(a(a(b(a(b(a(a(a(b(x1)))))))))) -> a(b(a(b(a(a(a(b(a(b(a(a(b(x1))))))))))))) By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: b(a(a(b(a(b(a(a(a(x))))))))) -> a(b(a(b(a(a(a(b(a(b(a(a(x)))))))))))) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: b(a(a(b(a(b(a(a(a(x))))))))) -> a(b(a(b(a(a(a(b(a(b(a(a(x)))))))))))) Q is empty. ---------------------------------------- (3) RFCMatchBoundsTRSProof (EQUIVALENT) Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R. The following rules were used to construct the certificate: b(a(a(b(a(b(a(a(a(x))))))))) -> a(b(a(b(a(a(a(b(a(b(a(a(x)))))))))))) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 41, 42, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158 Node 41 is start node and node 42 is final node. Those nodes are connected through the following edges: * 41 to 103 labelled a_1(0)* 42 to 42 labelled #_1(0)* 103 to 104 labelled b_1(0)* 104 to 105 labelled a_1(0)* 105 to 106 labelled b_1(0)* 106 to 107 labelled a_1(0)* 107 to 108 labelled a_1(0)* 108 to 109 labelled a_1(0)* 109 to 110 labelled b_1(0)* 109 to 137 labelled a_1(1)* 110 to 111 labelled a_1(0)* 111 to 112 labelled b_1(0)* 111 to 114 labelled a_1(1)* 112 to 113 labelled a_1(0)* 113 to 42 labelled a_1(0)* 114 to 115 labelled b_1(1)* 115 to 116 labelled a_1(1)* 116 to 117 labelled b_1(1)* 117 to 118 labelled a_1(1)* 118 to 119 labelled a_1(1)* 119 to 120 labelled a_1(1)* 120 to 121 labelled b_1(1)* 120 to 148 labelled a_1(2)* 121 to 122 labelled a_1(1)* 122 to 123 labelled b_1(1)* 122 to 114 labelled a_1(1)* 123 to 124 labelled a_1(1)* 124 to 42 labelled a_1(1)* 137 to 138 labelled b_1(1)* 138 to 139 labelled a_1(1)* 139 to 140 labelled b_1(1)* 140 to 141 labelled a_1(1)* 141 to 142 labelled a_1(1)* 142 to 143 labelled a_1(1)* 143 to 144 labelled b_1(1)* 143 to 148 labelled a_1(2)* 144 to 145 labelled a_1(1)* 145 to 146 labelled b_1(1)* 145 to 114 labelled a_1(1)* 146 to 147 labelled a_1(1)* 147 to 120 labelled a_1(1)* 148 to 149 labelled b_1(2)* 149 to 150 labelled a_1(2)* 150 to 151 labelled b_1(2)* 151 to 152 labelled a_1(2)* 152 to 153 labelled a_1(2)* 153 to 154 labelled a_1(2)* 154 to 155 labelled b_1(2)* 154 to 148 labelled a_1(2)* 155 to 156 labelled a_1(2)* 156 to 157 labelled b_1(2)* 156 to 114 labelled a_1(1)* 157 to 158 labelled a_1(2)* 158 to 120 labelled a_1(2) ---------------------------------------- (4) YES